Abstract
We defined in Chapter 1 (Definition 1.17) the notion of a Poisson mapping or morphism (as well as that of an automorphism or equivalence) for reasons of reference. Now, we shall discuss this notion in more detail, and use it in the study of the process of defining a Poisson structure on a manifold TV from a mapping ϕ: M → N, if M is endowed with a Poisson structure w. Such a process is possible in some interesting cases. Furthermore, this process is generalized in a procedure known as the reduction of a Poisson structure and, particularly, reductions appear in connection with group actions and momentum mappings.
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© 1994 Springer Basel AG
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Vaisman, I. (1994). Poisson Morphisms, Coinduced Structures, Reduction. In: Lectures on the Geometry of Poisson Manifolds. Progress in Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8495-2_8
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DOI: https://doi.org/10.1007/978-3-0348-8495-2_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9649-8
Online ISBN: 978-3-0348-8495-2
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